116. Air flows at the rate of 1.5 m³/s through a horizontal pipe with a gradually reducing crosssection as shown in the figure. The two crosssections of the pipe have diameters of 400 mm and 200 mm. Take the air density as 1.2 kg/m³ and assume inviscid incompressible flow. The change in pressure (p_{2 – p1) (in kPa) between sections 1 and 2 is}
     

1. 1. –1.28

   
   
   

   2. 2.56

   
   
   

   3. –2.13

   
   
   

   4. 1.28

   
   
   

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1. View Hint View Answer Discuss in Forum

   P1	+	V1²	+ Z1 =	P2	+	V2²	+ Z2 [Z = constant]
   δg		2g		δg		2g

   
   

   A1 =	π	× 0.4² = 0.1256 m²
   	2

   
   

   A2 =	π	× 0.2² = 0.314 m²
   	4

   
   

   P2 − P1	=	V1² − V2²
   δg		2g

   
   

   P2 − P1	=	1		Q2	−	Q2
   1.2		2		A1²		A2²

   
   

   P2 − P1 = 0.6 × (1.5)²		1	−	1
   		A1²		A2²

   
   

   P2 − P1 = 1.35		1	−	1
   		0.01577		0.00985

   
   = 1.35 [63.41 – 1015.22]
   = –1.28 ×10³ Pascal
   = – 1.28 kPa
   

   Correct Option: A

   P1	+	V1²	+ Z1 =	P2	+	V2²	+ Z2 [Z = constant]
   δg		2g		δg		2g

   
   

   A1 =	π	× 0.4² = 0.1256 m²
   	2

   
   

   A2 =	π	× 0.2² = 0.314 m²
   	4

   
   

   P2 − P1	=	V1² − V2²
   δg		2g

   
   

   P2 − P1	=	1		Q2	−	Q2
   1.2		2		A1²		A2²

   
   

   P2 − P1 = 0.6 × (1.5)²		1	−	1
   		A1²		A2²

   
   

   P2 − P1 = 1.35		1	−	1
   		0.01577		0.00985

   
   = 1.35 [63.41 – 1015.22]
   = –1.28 ×10³ Pascal
   = – 1.28 kPa
   

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117. Within a boundary layer for a steady incompressible flow, the Bernoulli equation

1. 1. holds because the flow is steady

   
   
   

   2. holds because the flow is incompressible

   
   
   

   3. holds because the flow is transitional

   
   
   

   4. does not hold because the flow is frictional

   
   
   

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1. View Hint View Answer Discuss in Forum

   Bernoulli equation does not hold because the flow is frictional.

   Correct Option: D

   Bernoulli equation does not hold because the flow is frictional.

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118. For a fluid element in a two dimensional flow field (x-y plane), if it will undergo

1. 1. Translation only

   
   
   

   2. Translation and rotation

   
   
   

   3. Translation and deformation

   
   
   

   4. Deformation only

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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119. Streamlines, path lines and streak lines are virtually identical for

1. 1. Uniform flow

   
   
   

   2. Flow of ideal fluids

   
   
   

   3. Steady flow

   
   
   

   4. Non uniform flow

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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120. A velocity field is given as
     VV^→ 3x²yî − 6xyzk̂
     where x, y, z are in m and V in m/s. Determine if
     (i) It represents an incompressible flow
     (ii) The flow is irrotational
     (iii) The flow is steady

1. 1. (ii)

   
   
   

   2. (i)

   
   
   

   3. (i) and (ii)

   
   
   

   4. (iii)

   
   
   

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1. View Hint View Answer Discuss in Forum

   V = 3x²î − 6xyzk̂
   

   ∂u	+	∂v	+	∂w	= 6xy + 0 − 6xy = 0
   ∂x		∂y		∂z

   
   Flow is incompressible
   

   wy =	1		∂u	−	∂w
   	2		∂z		∂x

   
   

   =	1	[0 − (−6yz)]
   	2

   
   w_y = 3yz
   Flow is rotational. Flow field is independent of time since terms does not include time ‘t’.

   Correct Option: A

   V = 3x²î − 6xyzk̂
   

   ∂u	+	∂v	+	∂w	= 6xy + 0 − 6xy = 0
   ∂x		∂y		∂z

   
   Flow is incompressible
   

   wy =	1		∂u	−	∂w
   	2		∂z		∂x

   
   

   =	1	[0 − (−6yz)]
   	2

   
   w_y = 3yz
   Flow is rotational. Flow field is independent of time since terms does not include time ‘t’.

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